Show that the residue of $\displaystyle \frac{\zeta^4(s)}{\zeta(2s)}\frac{x^{s+1}}{s(s+1)}$ at $\displaystyle s=1$ takes the form $\displaystyle x^2P(\log{x})$, where $\displaystyle P$ is a cubic polynomial. (Here, $\displaystyle \zeta(s)$ refers to the Riemann zeta-function.)